ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 30 Nov 2022 07:46:13 GMT2022-11-30T07:46:13Z5021- Test statistics for prospect and Markowitz stochastic dominances with applicationshttps://scholarbank.nus.edu.sg/handle/10635/125063Title: Test statistics for prospect and Markowitz stochastic dominances with applications
Authors: Bai, Z.; Li, H.; Liu, H.; Wong, W.-K.
Abstract: Levy and Levy (2002, 2004) extend the stochastic dominance (SD) theory for risk averters and risk seekers by developing the prospect SD (PSD) and Markowitz SD (MSD) theory for investors with S-shaped and reverse S-shaped (RS-shaped) utility functions, respectively. Davidson and Duclos (2000) develop SD tests for risk averters whereas Sriboonchitra et al. (2009) modify their statistics to obtain SD tests for risk seekers. In this paper, we extend their work by developing new statistics for both PSD and MSD of the first three orders. These statistics provide a tool to examine the preferences of investors with S-shaped utility functions proposed by Kahneman and Tversky (1979) in their prospect theory and investors with RS-shaped investors proposed by Markowitz (1952a). We also derive the limiting distributions of the test statistics to be stochastic processes. In addition, we propose a bootstrap method to decide the critical points of the tests and prove the consistency of the bootstrap tests. To illustrate the applicability of our proposed statistics, we apply them to study the preferences of investors with the corresponding S-shaped and RS-shaped utility functionsvis-à-visreturns on iShares andvis-à-visreturns of traditional stocks and Internet stocks before and after the Internet bubble. © 2011 The Author(s). The Econometrics Journal © 2011 Royal Economic Society.
Fri, 01 Jul 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1250632011-07-01T00:00:00Z
- Asymptotic properties of eigenmatrices of a large sample covariance matrixhttps://scholarbank.nus.edu.sg/handle/10635/125049Title: Asymptotic properties of eigenmatrices of a large sample covariance matrix
Authors: Bai, Z.D.; Liu, H.X.; Wong, W.K.
Abstract: Let Sn = 1/n XnXn where Xn = {X ij} is a p × n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Yn(t1, t 2,σ)=√p(xn(t1) *(Sn +σI)-1xn(t2)-x n(t1)*xn(t2)m n(σ)) in which σ > 0 and mn(σ)= ∫dFyn(x)/x+σ where Fyn(x) is the Marčenko-Pastur law with parameter yn = p/n; which converges to a positive constant as n → ∞ and xn(t1) and xn(t2) are unit vectors in ℂp, having indices t 1 and t2, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence Yn(t1, t2, σ) converges weakly to a (2m + 1)-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of S n is asymptotically close to that of a Haar-distributed unitary matrix. © 2011 Institute of Mathematical Statistics.
Sat, 01 Oct 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1250492011-10-01T00:00:00Z